Discrete element method

A discrete element method (DEM), also called a distinct element method is any of a family of numerical methods for computing the motion and effect of a large number of small particles. Though DEM is very closely related to molecular dynamics, the method is generally distinguished by its inclusion of rotational degrees-of-freedom as well as stateful contact and often complicated geometries (including polyhedra). With advances in computing power and numerical algorithms for nearest neighbor sorting, it has become possible to numerically simulate millions of particles on a single processor. Today DEM is becoming widely accepted as an effective method of addressing engineering problems in granular and discontinuous materials, especially in granular flows, powder mechanics, and rock mechanics. Recently, the method was expanded into the Extended Discrete Element Method taking thermodynamics and coupling to CFD and FEM into account.

Discrete element methods are relatively computationally intensive, which limits either the length of a simulation or the number of particles. Several DEM codes, as do molecular dynamics codes, take advantage of parallel processing capabilities (shared or distributed systems) to scale up the number of particles or length of the simulation. An alternative to treating all particles separately is to average the physics across many particles and thereby treat the material as a continuum. In the case of solid-like granular behavior as in soil mechanics, the continuum approach usually treats the material as elastic or elasto-plastic and models it with the finite element method or a mesh free method. In the case of liquid-like or gas-like granular flow, the continuum approach may treat the material as a fluid and use computational fluid dynamics. Drawbacks to homogenization of the granular scale physics, however, are well-documented and should be considered carefully before attempting to use a continuum approach.

Contents

The various branches of the DEM family are the distinct element method proposed by Cundall in 1971, the generalized discrete element method proposed by Williams, Hocking and Mustoe in 1985, the discontinuous deformation analysis (DDA) proposed by Shi in 1988 and the finite-discrete element method concurrently developed by several groups (e.g., Munjiza and Owen). The general method was originally developed by Cundall in 1971 to problems in rock mechanics. The theoretical basis of the method was established by Sir Isaac Newton in 1697. Williams, Hocking and Mustoe in 1985 showed that DEM could be viewed as a generalized finite element method. Its application to geomechanics problems is described in the book Numerical Methods in Rock Mechanics, by Pande, G., Beer, G. and Williams, J.R.. The 1st, 2nd and 3rd International Conferences on Discrete Element Methods have been a common point for researchers to publish advances in the method and its applications. Journal articles reviewing the state of the art have been published by Williams, Bicanic, and Bobet et al. (see below). A comprehensive treatment of the combined Finite Element-Discrete Element Method is contained in the book The Combined Finite-Discrete Element Method by Munjiza.

A DEM-simulation is started by first generating a model, which results in spatially orienting all particles and assigning an initial velocity. The forces which act on each particle are computed from the initial data and the relevant physical laws and contact models. Generally, a simulation consists of three parts: the initialization, explicit time-stepping, and post-processing. The time-stepping usually requires a nearest neighbor sorting step to reduce the number of possible contact pairs and decrease the computational requirements; this is often only performed periodically.

The following forces may have to be considered in macroscopic simulations:

All these forces are added up to find the total force acting on each particle. An integration method is employed to compute the change in the position and the velocity of each particle during a certain time step from Newton's laws of motion. Then, the new positions are used to compute the forces during the next step, and this loop is repeated until the simulation ends.

When long-range forces (typically gravity or the Coulomb force) are taken into account, then the interaction between each pair of particles needs to be computed. The number of interactions, and with it the cost of the computation, increases quadratically with the number of particles. This is not acceptable for simulations with large number of particles. A possible way to avoid this problem is to combine some particles, which are far away from the particle under consideration, into one pseudoparticle. Consider as an example the interaction between a star and a distant galaxy: The error arising from combining all the stars in the distant galaxy into one point mass is negligible. So-called tree algorithms are used to decide which particles can be combined into one pseudoparticle. These algorithms arrange all particles in a tree, a quadtree in the two-dimensional case and an octree in the three-dimensional case.

However, simulations in molecular dynamics divide the space in which the simulation take place into cells. Particles leaving through one side of a cell are simply inserted at the other side (periodic boundary conditions); the same goes for the forces. The force is no longer taken into account after the so-called cut-off distance (usually half the length of a cell), so that a particle is not influenced by the mirror image of the same particle in the other side of the cell. One can now increase the number of particles by simply copying the cells.

Following the work by Munjiza and Owen, the combined finite-discrete element method has been further developed to various irregular and deformable particles in many applications including pharmaceutical tableting,[1] packaging and flow simulations,[2] and impact analysis.[3]

DEM can be used to simulate a wide variety of granular flow and rock mechanics situations. Several research groups have independently developed simulation software that agrees well with experimental findings in a wide range of engineering applications, including adhesive powders, granular flow, and jointed rock masses.

DEM allows a more detailed study of the micro-dynamics of powder flows than is often possible using physical experiments. For example, the force networks formed in a granular media can be visualized using DEM. Such measurements are nearly impossible in experiments with small and many particles.

Disadvantages

The maximum number of particles, and duration of a virtual simulation is limited by computational power. Typical flows contain billions of particles, but contemporary DEM simulations on large cluster computing resources have only recently been able to approach this scale for sufficiently long time (simulated time, not actual program execution time).

ESyS-Particle ESyS-Particle is a high-performance computing implementation of the Discrete Element Method released under the Open Software License v3.0. To date, development focus is on geoscientific applications including granular flow, rock breakage and earthquake nucleation. ESyS-Particle includes a Python scripting interface providing flexibility for simulation setup and real-time data analysis. The DEM computing engine is written in C++ and parallelised using MPI, permitting simulations of more than 1 million particles on clusters or high-end workstations.

GranOO GranOO is a robust and versatil workench devoted to build 3D dynamic simulations based on the Discrete Element Method (DEM). It is written in C++ under GNU-Linux and distributed under the free GPLv3 license.

LMGC90 Open platform for modelling interaction problems between elements including multi-physics aspects based on an hybrid or extended FEM – DEM discretization, using various numerical strategies as MD or NSCD.

Pasimodo PASIMODO is a program package for particle-based simulation methods. The main field of application is the simulation of granular media, such as sand, gravel, granulates in chemical engineering and others. Moreover it can be used for the simulation of many other Lagrangian methods, e.g. fluid simulation with Smoothed-Particle-Hydrodynamics.

Yade Yet Another Dynamic Engine (historically related to SDEC), modular and extensible toolkit of DEM algorithms written in c++. Tight integration with Python gives flexibility to simulation description, real-time control and post-processing, and allows introspection of all internal data. Can run in parallel on shared-memory machines using OpenMP.

MechSys Although it was initially a package dedicated to the FEM method, nowadays it also contains a DEM module. It uses both spherical elements and spheropolyhedra to model collision of particles with general shapes. Both elastic and cohesive forces are included to model damage and fracture processes. Parallelization is achieved mostly by POSIX threads. There is also a module dealing with the coupling between DEM and the Lattice Boltzmann Method (LBM).

Commercially available DEM software packages:

Bulk Flow Analyst (Applied DEM) General-purpose 3D DEM tool for mechanical engineering applications. Imports many types of 3D modelling files (including DXF, IGES, and STEP) and integrates with AutoCAD and SolidWorks as well as providing its own 3D interface.

Chute Analyst (Overland Conveyor Company) 3D DEM tool for transfer chute engineering applications. Imports many types of 3D modelling files (including DXF, IGES, and STEP) and integrates with AutoCAD and SolidWorks as well as providing its own 3D interface.

ROCKY Fast and accurate 3D DEM program that simulates the granular flow behavior of different shaped and sized particles within a conveyor chute, mill, or other materials handling equipment. It has a modern GUI and many unique features such as true non-round particle shapes, particle breakage, 3D surface wear, 6 degree-of-freedom, integrates with ANSYS FEA and CFD and parallelizes well on multi-core CPU and GPU.

Newton is a general purpose Discrete Element Method (DEM) simulation package used model the three dimensional behavior of complex material flows developed by Advanced Conveyor Technologies Inc (AC-Tek)